Your mother's well-diversified portfolio has an expected return of 12.0% and a beta of 1.20.She is in the process of buying 100 shares of Safety Corp.at $10 a share and adding it to her portfolio.Safety has an expected return of 15.0% and a beta of 2.00.The total value of your current portfolio is $9,000.What will the expected return and beta on the portfolio be after the purchase of the Safety stock?
$ \quad\underline{\text {Ip}}\quad\quad\underline{\text {bp}}$
A) $11.69 \% ; 1.22$
B) $12.30 \% ; 1.28$
C) $12.92 \% ; 1.34$
D) $13.56 \% ; 1.41$
E) $14.24 \% ; 1.48$

Question

Your mother's well-diversified portfolio has an expected return of 12.0% and a beta of 1.20.She is in the process of buying 100 shares of Safety Corp.at $10 a share and adding it to her portfolio.Safety has an expected return of 15.0% and a beta of 2.00.The total value of your current portfolio is $9,000.What will the expected return and beta on the portfolio be after the purchase of the Safety stock? 
$ \quad\underline{\text {Ip}}\quad\quad\underline{\text {bp}}$
A) $11.69 \% ; 1.22$
B) $12.30 \% ; 1.28$
C) $12.92 \% ; 1.34$
D) $13.56 \% ; 1.41$
E) $14.24 \% ; 1.48$

Quizplus · Accepted Answer

First, let's calculate the initial portfolio weighted average beta:

Portfolio Beta = (0.98 x 1.20) + (0.02 x 0) = 1.176

Next, let's calculate the expected return on the Safety Corp purchase:

Expected Return on Safety Corp = 15.0%

Then, we can calculate the new portfolio weighted average beta:

New Portfolio Beta = [(0.98 x 1.20) + (0.02 x 2.00)] = 1.184

Finally, we can calculate the new portfolio's expected return using the following formula:

New Portfolio Expected Return = Expected Return of Initial Portfolio x Weight of Initial Portfolio + Expected Return on Safety Corp x Weight of Safety Corp

New Portfolio Expected Return = (0.98 x 12.0%) + (0.02 x 15.0%) = 11.76% + 0.30% = 12.06%

Therefore, the expected return on the portfolio after purchasing Safety Corp stock is 12.06% and the beta is 1.184.

The best choice is B.

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